Replacing the soil would absolutely be a good idea, and you could also cut it a lot back. In my opinion there is hope! :)

At first glance I thought your plant was a Ming...

Yes, cut it back, shape to your desire...it should grow compact. Toni

Where do you live?
If a colder area, best to wait until Summer to re-pot and/or prune.

For the time being, I would fertilize the plant.

Josh

What josh said - plus, I would flush the soil and pot-up slightly after disturbing the outer part of the root ball. In order of what I would do to rejuvenate the plant:

A) Flush the soil thoroughly by pouring at least 10 times the volume of the pot it's in through the soil. This is like hitting your fertilizer 'reset' button because it rinses all the excess salts from the soil that have built up over time.
B) remove the plant from that pot and move it to one only slightly larger. Use a nut pick or screwdriver to tease any circling roots from the outside of the root mass before potting up. BTW, the 'potting up' is only a temporary measure to help you get the plant through to a more appropriate time to repot, which like Josh said is summer.
C) Fertilize immediately after you flush the soil or wait until it needs its first watering. Use something with a 3:1:2 NKP ratio. Ratios are different than NPK %s. 24-8-16, 12-4-8, and 9-3-6 are all examples of 3:1:2 ratios. I use Foliage-Pro 9-3-6 by Dyna-Grow because it has ALL the nutrients essential to normal growth (most soluble fertilizers lack several important nutrients - especially Ca and Mg), in a favorable ratio, and it derives most of its N from nitrate sources (not from urea) which helps to keep your plants compact and from getting leggy.
D) Around Father's Day, I would repot into a good soil - one that allows you to water correctly.
E) When there is evidence the plant is pushing new growth, I would cut it back hard. If the plant is healthy, it will tolerate a hard pruning w/o complaint. Something is going on with my server right now, painfully slow, so I can't show pictures of a hard pruning of a China doll - perhaps when things are squared away there.
F) I would repot it at regular intervals - probably every 2 years - 3 years max. If you follow the steps, there is no reason you can't keep your tree healthy and beautiful long enough to pass it down a generation or two, or more.

Al

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Thanks for the feedback, everyone. If all goes well I'll post a follow-up pic next year. (maybe by then I'll be able to post pics right-side-up).